**Finding all three-digit numbers divisible by 13**

To find all three-digit natural numbers that are divisible by 13, we can start by finding the smallest three-digit number divisible by 13 and then incrementally adding 13 until we reach the largest three-digit number divisible by 13.

The smallest three-digit number is 100, and we can divide it by 13 to check if it is divisible evenly. If the remainder is 0, then it is divisible by 13. If not, we can add 13 to it and repeat the process until we find a number that is divisible by 13.

We can use the following steps to find all three-digit numbers divisible by 13:

1. Start with the smallest three-digit number, 100.
2. Divide 100 by 13 to check if it is divisible evenly. The remainder is 0, so it is divisible.
3. Add 13 to 100 to get the next number, 113.
4. Divide 113 by 13 to check if it is divisible evenly. The remainder is not 0.
5. Repeat the process by adding 13 to 113, resulting in 126.
6. Divide 126 by 13 to check if it is divisible evenly. The remainder is 0, so it is divisible.
7. Continue this process until we reach the largest three-digit number.

We can summarize the steps in an algorithm:

1. Set the smallest three-digit number, 100, as the starting point.
2. Check if the number is divisible by 13 by finding the remainder.
3. If the remainder is 0, add the number to the sum of all divisible numbers.
4. Increment the number by 13.
5. Repeat steps 2-4 until the number becomes larger than the largest three-digit number.

**Calculating the sum of all three-digit numbers divisible by 13**

Now that we have found all the three-digit numbers divisible by 13, we can calculate their sum.

We can use the formula for the sum of an arithmetic series to find the sum of all the numbers. The formula is:

Sum = (n/2)(first term + last term)

In this case, the first term is the smallest three-digit number divisible by 13, and the last term is the largest three-digit number divisible by 13. The number of terms, n, can be calculated by:

n = (last term - first term)/common difference + 1

In this case, the common difference is 13 since we are adding 13 to each number to find the next one.

We can substitute the values into the formulas to calculate the sum:

- First term: Smallest three-digit number divisible by 13
- Last term: Largest three-digit number divisible by 13
- Common difference: 13
- Number of terms: (last term - first term)/common difference + 1

Once we have calculated the sum using the formulas, we will have the sum of all three-digit natural numbers that are divisible by 13.